In my experience a standard chess software such as Fritz - at least the 8 version running on chessbase database, is very bad for problems. If it sees a #4, it stops here and does not search for shorter mate. I have also noticed that it does not foresee defences based on underpromotion.
There is also the special case of e.p. key, which I know mrmip is fond of, this computer softwares definitely do not see._________________"Si tu vois un bon coup, ne le joue pas!!" - Philippe Bichu (after Em. Lasker)

Thanks for the explanation. Clearly the computer does not search through all alternatives. Its suggestion c2-c3 indeed mates in 4 moves, but the given solution mates in 3 as reguired.

If you look to the 'Navigate solution' you will see that the alternative of exchanging the rook is also covered and results mate in 3 as well.

I suggest you put the first move and any possible black defence move into the computer and look for mate in 2. Surely it can find that ?_________________There are only three kinds of chessplayers - those who can count and those who cannot....

I resetted the computer to its default algorithm (it has multiple search algorithms) which is the strongest, and it found the mate in 3 in a second. So it was different algorithm that prevented it fidning mate in 3 but it found mate in 4.

No,no I will not forget - But here is a philosophical dilemma:
If a problem is mate in 3, can it also be a mate in 4?

Because a problem inherently reguires both parties to make very best moves, then when white makes a correct first move (key) the problem terminates after white's 3rd move and s/he never gets to play the 4th move - so the mate in 4 is impossible - No?_________________There are only three kinds of chessplayers - those who can count and those who cannot....

is the question always posed to find a mate with best possible moves, or simply to find a mate? With best possible moves the shortest path is reached, but if not best possible then any path is possible as long as it is forced, and in this case the mate in 4 is possible since it is forced moves from black's point of view, even if white did not choose the best possible first move.